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Why does Implied Risk Aversion Smile?

Author

Listed:
  • Alexandre Ziegler

    (University of Lausanne and FAME)

Abstract

A few recent papers have derived estimates of the representative agent's risk aversion by comparing the statistical density of asset returns and the state-price density. The implied risk aversion estimates obtained in these studies are puzzling, exhibiting (i) pronounced U-shaped patterns (a "smile") and (ii) negative values. This paper analyzes three potential explanations for these phenomena: (i) heterogeneity in investor preferences, (ii) difficulties in estimating agents' beliefs and (iii) heterogeneous beliefs among agents. Our results show that preferences alone cannot explain the patterns reported in the literature. Misestimation of investors' beliefs caused by nonstationarity of the return process cannot explain the smile either. The patterns of beliefs misestimation required to generate the empirical implied risk aversion estimates found in the literature suggest that heterogeneous beliefs are the most likely cause of the smile.

Suggested Citation

  • Alexandre Ziegler, 2002. "Why does Implied Risk Aversion Smile?," FAME Research Paper Series rp47, International Center for Financial Asset Management and Engineering.
    • Handle: RePEc:fam:rpseri:rp47
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    File URL: http://www.swissfinanceinstitute.ch/rp47.pdf
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    References listed on IDEAS

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    1. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-240, April.
    2. Evan W. Anderson & Eric Ghysels & Jennifer L. Juergens, 2005. "Do Heterogeneous Beliefs Matter for Asset Pricing?," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 875-924.
    3. Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.
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    6. Poon, Ser-Huang, 2005. "Asset Pricing in Discrete Time: A Complete Markets Approach," OUP Catalogue, Oxford University Press, number 9780199271443.
    7. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    8. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    9. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    10. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    11. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    12. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    13. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    14. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
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    Cited by:

    1. Daniel Giamouridis, 2005. "Inferring option-implied investors' risk preferences," Applied Financial Economics, Taylor & Francis Journals, vol. 15(7), pages 479-488.

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    More about this item

    Keywords

    asset pricing; state-price density; heterogeneous preferences; heterogeneous beliefs; implied risk aversion;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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